I had a look through their list of size-adjusted maps and found it curious that you can get population size, and you can get land area, and you can get urbanization rate; but they don't have one for population density.

You can sort of rough it out by looking at the population size map and running through the countries that look a bit deflated or a bit inflated; but that's not wildly precise.

As it happens, penguins are terrifyingly skilled in census and electoral fraud(incidentally, this is why the traditional costume of the plutocratic class is made to resemble the penguin's plumage, it's an attempt to gain the animal's powers of undue influence by sympathetic magic). Were it not for geographical constraints on their range, we would probably all be living under an avian oligarchy.

Not very good choices for area mapping. The united states population is twice as much as Mexico and yet the area of the Alaska appears to displace area away from the lower 48 in a way that implies Mexico's population is similar. Population density to area would definitely be better as mentioned earlier.

Alaska appears to displace area away from the lower 48 in a way that implies Mexico's population is similar.

I think at some point, they had to make a decision about the level of granularity they wanted to present, and chose to go with nations.

Consider the United States as an example. If we were to map the states of the US in a similar way, the coastal states would be inflated considerably from their actual size while the intermountain west (basically the Mountain Time zone) would shrink down to pinpricks. The map might be recognizable to someone familiar with the states of the US, but might as well be an inkblot to a Ugandan*.

Taking the granularity a step further, to the level of counties would make my own state, Oklahoma, nearly unrecognizable even to longtime residents. Half of the population lives in just 3 of the 77 counties.

The tl;dr (too late, I know): I'm willing to let the map-makers lump Alaska in with the whole of the US, rather than treat it as a separate entity.

*Ugandan was an arbitrary choice for someone who lives half a world away and has no need to be familiar with US internal boundaries.